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Time Space Domain Decomposition Methods for Reactive Transport --- Application to CO2 Geological Storage

Abstract : Reactive transport modelling is a basic tool to model chemical reactions and flow processes in porous media. A totally reduced multi-species reactive transport model including kinetic and equilibrium reactions is presented. A structured numerical formulation is developed and different numerical approaches are proposed. Domain decomposition methods offer the possibility to split large problems into smaller subproblems that can be treated in parallel. The class of Schwarz-type domain decomposition methods that have proved to be high-performing algorithms in many fields of applications is presented with a special emphasis on the geometrical viewpoint. Numerical issues for the realisation of geometrical domain decomposition methods and transmission conditions in the context of finite volumes are discussed. We propose and validate numerically a hybrid finite volume scheme for advection-diffusion processes that is particularly well-suited for the use in a domain decomposition context. Optimised Schwarz waveform relaxation methods are studied in detail on a theoretical and numerical level for a two species coupled reactive transport system with linear and nonlinear coupling terms. Wellposedness and convergence results are developed and the influence of the coupling term on the convergence behaviour of the Schwarz algorithm is studied. Finally, we apply a Schwarz waveform relaxation method on the presented multi-species reactive transport system.
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Contributor : Florian Haeberlein Connect in order to contact the contributor
Submitted on : Friday, October 21, 2011 - 1:47:23 PM
Last modification on : Wednesday, October 27, 2021 - 2:52:23 PM
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  • HAL Id : tel-00634507, version 1


Florian Haeberlein. Time Space Domain Decomposition Methods for Reactive Transport --- Application to CO2 Geological Storage. Mathematics [math]. Université Paris-Nord - Paris XIII, 2011. English. ⟨tel-00634507⟩



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